GMAT Question  >  What is the area of isosceles triangle X? The... Save

Related Test

What is the area of isosceles triangle X?
  1. The length of the side opposite the single largest angle in the triangle is 6cm
  2. The perimeter of triangle X is 16cm
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
  • d)
    EACH statement ALONE is sufficient to answer the question asked;
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Correct answer is option 'C'. Can you explain this answer?

Answers

  1. In a triangle, the side opposite the largest angle will be the longest. Correspondingly, the side opposite the smallest angle will be the shortest.
  2. Evaluate Statement (1) alone.
    1. The side opposite the single largest angle must be the single largest side in the triangle. Since an isosceles triangle contains two equal sides and two equal angles yet we know that a "single largest angle" exists, the side opposite the single largest angle cannot be one of these equal sides. If the longest side of an isosceles triangle were one of its equal sides, both angles opposite the equal sides would have equal measurement and there would be no single largest angle as Statement (1) indicates there must be.
    2. The single largest side must be the base since the two other angles will have equivalent measurements and thus the length of the sides opposite them will be equivalent. The two equal sides must be less than 6cm (otherwise, the angle opposite the base would not be the single largest angle in the triangle). To reiterate, the two angles opposite the equivalent sides must be smaller than the angle opposite the base (otherwise the angle opposite 6cm side would not be the single largest angle).
    3. The two equal sides must be longer than 3cm. Otherwise a closed triangle could not be formed (i.e., the lines would not connect).
    4. Draw a diagram with the information we know:


      AC = 6
      3cm < AB < 6cm
      3cm < BC < 6cm
    5. Although we know the base, we know nothing about the height, BD. Without knowing that a definitive value for the height exists, we cannot calculate the area of the triangle.
    6. Statement (1) is NOT SUFFICIENT.
  3. Evaluate Statement (2) alone.
    1. Since triangle X is an isosceles triangle, the perimeter is formed by adding two equal sides and a third side. Set up an equation to reflect this:
      2L + N = 16 where L is the length of the equivalent sides of the triangle and N is the length of the other side.
    2. There are many different combinations of L and N that would give a different area. Assume that N is the base:
      If N = 4 and L = 6, then the height of the triangle (via the Pythagorean theorem) would be the square root of 32, which is 5.65
      If N = 5 and L = 5.5, then the height of the triangle (via the Pythagorean theorem) would be the square root of 24, which is 4.89.
    3. Without being able to determine that a definitive value for the base and height exists, we cannot calculate the area of the triangle.
    4. Statement (2) is NOT SUFFICIENT.
  4. Evaluate Statements (1) and (2) together.
    1. Write equations that are derived from the information in both Statements:
      (1) Base = 6cm
      (2) 2L + B = 16
    2. Combine the two equations:
      2L + 6 = 16
      L = 5
    3. We now have a right triangle formed by half the base (AD = 3), the height (BD = unknown), and an equal side (AB = 5).


      AC = 6
      AD = 3
      AB = BC = 5
      Note: Since the triangle is isosceles, the height (or line BD) must perfectly bisect the base. This is because angles A and C are equal and sides AB and BC are equal. Further, angle D is right since it is the height and the height is by definition a right angle.
    4. Through the Pythagorean theorem, BD must equal 4:
      (AD)2 + (BD)2 = (AB)2
      9 + (BD)2 = 25
      (BD)2 = 16
      BD = 4
    5. The area of triangle X must be (1/2)Base x Height = 3(4) = 12
    6. Statements (1) and (2), when taken together, are SUFFICIENT.
  5. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2), when taken together are SUFFICIENT, answer C is correct.

View courses related to this question
Explore GMAT courses
Explore GMAT courses
View courses related to this question
1 Crore+ students have signed up on EduRev. Have you?

Similar GMAT Doubts

  • The area of a rectangle is 28 square centimeter. What is the perimeter of t... more

  • 1 Answer

  • Directions: Each GMAT Data Sufficiency problem consists of a question and t... more

  • 1 Answer

  • Directions: Each GMAT Data Sufficiency problem consists of a question and t... more

  • 1 Answer

Question Description
What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
Solutions for What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What is the area of isosceles triangle X? The length of the side opposite the single largest angle in the triangle is 6cm The perimeter of triangle X is 16cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
In a triangle, the side opposite the largest angle will be the longest. Correspondingly, the side opposite the smallest angle will be the shortest. Evaluate Statement (1) alone. The side opposite the single largest angle must be the single largest side in the triangle. Since an isosceles triangle contains two equal sides and two equal angles yet we know that a "single largest angle" exists, the side opposite thesinglelargest angle cannot be one of these equal sides. If the longest side of an isosceles triangle were one of its equal sides, both angles opposite the equal sides would have equal measurement and there would be nosinglelargest angle as Statement (1) indicates there must be. The single largest side must be the base since the two other angles will have equivalent measurements and thus the length of the sides opposite them will be equivalent. The two equal sides must be less than 6cm (otherwise, the angle opposite the base would not be the single largest angle in the triangle). To reiterate, the two angles opposite the equivalent sides must be smaller than the angle opposite the base (otherwise the angle opposite 6cm side would not be the single largest angle). The two equal sides must be longer than 3cm. Otherwise a closed triangle could not be formed (i.e., the lines would not connect). Draw a diagram with the information we know: AC = 6 3cm < AB < 6cm 3cm < BC < 6cm Although we know the base, we know nothing about the height, BD. Without knowing that a definitive value for the height exists, we cannot calculate the area of the triangle. Statement (1) is NOT SUFFICIENT. Evaluate Statement (2) alone. Since triangle X is an isosceles triangle, the perimeter is formed by adding two equal sides and a third side. Set up an equation to reflect this: 2L + N = 16 where L is the length of the equivalent sides of the triangle and N is the length of the other side. There are many different combinations of L and N that would give a different area. Assume that N is the base: If N = 4 and L = 6, then the height of the triangle (via the Pythagorean theorem) would be the square root of 32, which is 5.65 If N = 5 and L = 5.5, then the height of the triangle (via the Pythagorean theorem) would be the square root of 24, which is 4.89. Without being able to determine that a definitive value for the base and height exists, we cannot calculate the area of the triangle. Statement (2) is NOT SUFFICIENT. Evaluate Statements (1) and (2) together. Write equations that are derived from the information in both Statements: (1) Base = 6cm (2) 2L + B = 16 Combine the two equations: 2L + 6 = 16 L = 5 We now have a right triangle formed by half the base (AD = 3), the height (BD = unknown), and an equal side (AB = 5). AC = 6 AD = 3 AB = BC = 5 Note: Since the triangle is isosceles, the height (or line BD) must perfectly bisect the base. This is because angles A and C are equal and sides AB and BC are equal. Further, angle D is right since it is the height and the height is by definition a right angle. Through the Pythagorean theorem, BD must equal 4: (AD)2+ (BD)2= (AB)2 9 + (BD)2= 25 (BD)2= 16 BD = 4 The area of triangle X must be (1/2)Base x Height = 3(4) = 12 Statements (1) and (2), when taken together, are SUFFICIENT. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2), when taken together are SUFFICIENT, answer C is correct.